A Universal Formula for the Stress-Tensor Contribution to Scalar Four-Point Functions

TL;DR

This paper presents a universal Mellin-space formula for scalar four-point functions in AdS/CFT, simplifying calculations of stress-tensor contributions and advancing towards computing four-point functions in N=4 super Yang-Mills theory.

Contribution

It introduces a universal, dimension-agnostic formula for graviton-exchange Witten diagrams using hypergeometric functions, aiding the proof of a longstanding conjecture and future computations.

Findings

Derived a universal formula involving 11 hypergeometric functions.

Expressed the result in terms of scalar-exchange D-functions.

Paves the way for computing stress-tensor four-point functions in N=4 sYM.

Abstract

We illustrate the power and efficiency of a recently uncovered Mellin-space approach to AdS/CFT correlation functions by providing a universal formula for the 4-scalar graviton-exchange Witten diagram, for arbitrary CFT-dual scaling dimensions. Our result keeps the space-time dimension generic as well, and is expressed as a combination of just 11 hypergeometric functions. Such hypergeometric functions are related to scalar-exchange diagrams. In particular, if reverse-engineered in terms of D-functions, this might be viewed as a first-step towards proving a long-standing conjecture by Dolan, Nirschl and Osborn pertaining to four-point correlators of chiral primary operators at strong coupling. Most importantly, the technology developed herein marks an additional development towards the long-anticipated computation of the four-point function of the N=4 sYM stress-tensor.